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Iterative methods for direction of arrival estimation of a signal at a receiver with a plurality of spatially separated sensor elements are described. A quantized estimate of the angle of arrival is obtained from a compressive sensing solution of a set of equations. The estimate is refined in a subsequent iteration by a computed error based a quantized estimate of the direction of arrival in relation to quantization points offset from the quantization points for the first quantized estimate of the angle of arrival. The iterations converge on an estimated direction of arrival.